The higher-order breather, periodic-wave, lump, rational soliton solutions and mixed solutions of the Hirota–Maccari (HM) system by virtue of the Kadomtsev–Petviashvili (KP) hierarchy reduction method are investigated in this work. Through analyzing the structural characteristics of periodic-wave solutions, we attain the quasi-periodic W(M)-shaped waves and two kinds of breathers. The mixed solutions that consist of the quasi-periodic W(M)-shaped waves and breathers are constructed. Further, by taking the long wave limit on the periodic-wave solutions, the semi-rational solutions are derived, which illustrate the interaction of the rational soliton, lump, quasi-periodic wave and breather. Characteristics of these mixed solutions are discussed graphically and the corresponding generating conditions are given. Especially, a new bound-state interaction composed of lump and breather is generated under the velocity resonance mechanism. This newfangled pattern is a beautiful phenomenon for the HM system.

在这项工作中，借助 Kadomtsev-Petviashvili (KP) 层次约简方法研究了 Hirota-Maccari (HM) 系统的高阶呼吸子、周期波、块、有理孤子解和混合解。通过分析周期波解的结构特征，我们得到了准周期W(M)型波和两种呼吸子。构造了由准周期 W(M) 形波和呼吸器组成的混合解。进一步，通过对周期波解取长波极限，推导了半有理解，说明了有理孤子、块、准周期波和呼吸子的相互作用。以图形方式讨论了这些混合溶液的特性，并给出了相应的生成条件。尤其，在速度共振机制下产生了由团块和呼吸子组成的新束缚态相互作用。这种新奇的模式对于 HM 系统来说是一个美丽的现象。